Alice challenges Bob for the following game:

First Bob takes 2⁹ numbers from the set {0,1,2,3,...,1024}, then Alice takes 2⁸ of the remaining numbers. Then Bob takes 2⁷ numbers and successively, until only two numbers remain. Alice will have to give Bob the difference between these two numbers in euros. What is the largest amount Bob can win, whatever Alice's strategy is?

Assuming that "whatever Alice's strategy is"  - means - Alice's strategy can be anything, even a poor one, then the maximum Bob can win is 1024 Euros.  This can happen many ways.  One way is as follows.  Bob takes 1 thru 512, Alice (with her bad strategy), takes 513 thru 768, then Bob and Alice continue in this consecutive way until only 0 and 1024 are left.

Posted by Kenny M on 2021-01-01 16:46:17